Known from the prior art is an apparatus for controlling the lateral offset of webs of material, including, as illustrated in FIGS. 1a and 1b, a roll for guiding a web of material, the roll being rotatably and laterally shiftably mounted via ball bearings on a continuous shaft connected to a fixed support. The lateral position of the web of material is measured via a detector. When the position of the web of material needs to be corrected, the roll can be shifted laterally on the fixed shaft via a servomotor during the advancement of the web. Provided for this purpose is a control unit that processes the signals from the detector and drives the actuator accordingly. Since the travel distance is limited, before the maximum travel distance is reached a lifting mechanism has to raise the web so the roll can be moved back into a neutral position without contacting the web. In the prior art, the lifting mechanism consists of a single roller that can be shifted pneumatically. For the above-stated reason, the apparatus is normally used according to the prior art in intermittent mode, including the following phases of operation: advancement of the web of material with simultaneous control of the lateral offset of the web, and halting of the web of material with lifting by the lifting mechanism and return of the roll to neutral position.